Abstract

Large scale, three dimensional computer simulations of a dense aggregative bed were performed to provide insight into the physics behind bubble formation in vertically vibrated granular materials in a shaker. As the shaker acceleration exceeds a critical value, turbulent fluctuations proportional to the particle size were produced to promote fractures at the interface between the gas and particles suspended in the gas near the bottom of the shaker. As the wave fronts pass, the solid fractures took the form of sharply defined regions of very low solids fraction (air cavities) that rose through the bed with a speed that depends on their size. The nucleation of bubbles is found to be of the heterogeneous type.

Figures

(a) Sketch of the shaker. The shaker is made of two concentric cylinders. The diameter of the inner cylinder is D=9.6cm, the radial gap size is r=0.625cm, and the initial height of the glass layer is L0. (b) Spherical glass balls with diameter dp=200μm were used. The initial height of the glass layer was 4cm, and the free surface is flat before the oscillations begin. Inset, the glass balls were randomly distributed with air filling the pore space.

(a) An instantaneous configuration of glass balls. Here, Γ=6.673, ω∕2π=20Hz, A0=0.42cm, and L0=4cm. Time is t=0.15s after shaking. (b) An instantaneous configuration of glass balls in free flight after t≈1s of shaking. (c) The bubbling sand. Here, Γ=8, ω∕2π=21.76Hz, A0=0.42cm, and L0=4cm. Time is t=1.2s after shaking. (d) The end of coalesce process. Time is t=1.5s after shaking. (e) The experimental result (reproduced with permission of R. P. Behringer). Here, Γ=8.79, ω∕2π=22.85Hz, A0=0.42cm, and L0=4cm. (f) The simulation result. Shown is an instantaneous configuration of glass balls. Here, Γ=9, ω∕2π=23.08Hz, A0=0.42cm, and L0=4cm.

(a) Typical temporal behavior of the dimensionless kinetic energy per particle in the bubbling sand. Here, Γ=8, ω∕2π=21.76Hz, A0=0.42cm, and L0=4cm. (b) Dimensionless average bubble area, S*, as a function of normalized acceleration, Γ*Γb=6.67. The circles are experimental results in Ref. 14, and the squares are the results of the simulation. The solid line is fitted by expression 1 in the text. Here, at least two types of fluidization phases can be recognized.

Return to: Air Cavities in a Vibrated Bed of Visco-Elastic Glass Balls

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